Maybe I shouldn't have started this blog now, not with everything that's been going on.

Trimester 3, Week 3, Advanced Mathematics, Meeting 2 continued: now I’ll go to the two blunders I mentioned last time that I made in two classes with the same students.

After discussing to them the co-factor method of solving for the determinant, I tried to demonstrate by asking two students to solve a four by four matrix using both methods.

They didn’t get the same answer, despite the fact that we looked through their computations step by step.

I just promised them that I would look at the solutions after the class.

When I did, it turned out that the traditional way of solving two by two and three by three matrices (sum of left leaning diagonals from the products of the elements minus the sum of the similar right leaning diagonals) couldn’t be applied for getting the determinants of larger (read: greater than three) matrices. So it turns out there is shortcut for those types of matrices.

A nearly parallel incident happened in my Electromagnetic Theory class a day or two before or after.

This was when I was making comparisons between the two methods for getting the cross product. One formula used the magnitudes of the two vectors involved and the sine of the angle between them. The other equation used the factor distribution of the components of the two vectors.

Again, I asked two students to solve the cross product of two vectors using each method.

Again, the final answers did not match.

It was getting embarrassing.

Unlike the other class though, I had the resources right there (read: the text book) to find out where I went wrong.

That’s when I saw that my expression for the multiplication of components was wrong.

The real equation, in fact, could be given as a three by three matrix, which made some of the same seven students also in my Advanced Mathematics class wail in mock fear and pain.

I should have known at the start that the formula was wrong since the cross product is a vector and therefore there should have been the three unit vectors in the terms.

In that sense I was also able to show them that the direction (two angles for three dimensions) could be determined by a more exact method than the right hand rule.

Next time I’ll talk about the rest of the third week of classes, and something about Friday that I decided not to talk about until it came up chronologically. And that’s it for today.